In recent years, spatiotemporal synchronisation within systems with multiple interacting components (Complex Systems), such as financial data, electroencephalographic (EEG) recordings and magnetoencephalographic (MEG) recordings, has been studied extensively, using the equal-time cross-correlation matrix. These Complex Systems are characterised by events such as Market Crashes or Seizures, which are associated with periods of hypersynchronisation. In this Thesis, the Risk Characterisation and Reduction of Complex Systems is studied, using the Cross-Correlation matrix to condense the system complexity. The systems studied display interactions between multivariate time series of varying granularities, including low frequency (Hedge Fund returns), medium frequency (Daily Stock returns) and high frequency (Intraday Stock returns & EEG seizure data). The information content of the correlation matrix between low-frequency Hedge Fund returns is investigated for the first time using Random Matrix Theory (RMT). The RMT filtered correlation matrix is shown to improve the risk-return profile of a portfolio of Hedge Funds. Through the use of the Wavelet transform, scaling properties of correlations are then investigated, with correlations calculated over longer horizons found to result in a better risk-return profile for a portfolio of Hedge Funds. Characterisation of market risk is then assessed, through the dynamics of the correlation structure and associated eigenspectrum for daily equity returns (medium frequency data), using a moving window approach. This novel characterisation, dependent on both large and small eigenvalue behaviour, is shown to be consistent across different time scales. Further, frequency dependent correlations were examined for medium and high-frequency intra-day stock returns using Wavelet multiscaling. Investigation of a comparative system example, specifically correlation scaling characteristics of high-frequency EEG Seizure data, revealed novel frequency dependent changes in the correlation structure between channels, which may be indicative of seizures. Large correlations were found between channels at high frequencies and conversely, smaller correlations at low frequencies during Seizures, with a corresponding switch in system energy. Our findings suggest that, even for the limited set of examples chosen, diverse applications demonstrate commonality, in terms of the interpretative power of time-series correlation structure. Through the integration of tools such as Random Matrix Theory, Wavelet multiscaling and eigenvalue analysis, we have shown the importance of the correlation matrix in risk characterisation and reduction. The potential for wider application of these methods in the detection of subtle triggers, giving advance warning of risky events, has also been demonstrated.